Questions: Determine the domain and the range of the piecewise function shown to the right. Then write an equation for the function A. The range is a list of numbers, -2,1,2 (Use a comma to separate answers as needed) B. The range is (Type your answer in interval notation) Write an equation for the function. Select the correct choice below and fill in the answer boxes to complete your choice. A. f(x)=, for ≤ x< , for ≤ x ≤ , for <x ≤ , for x< . 3. for x= - for x>

Determine the domain and the range of the piecewise function shown to the right. Then write an equation for the function
A. The range is a list of numbers, -2,1,2
(Use a comma to separate answers as needed)
B. The range is
(Type your answer in interval notation)
Write an equation for the function. Select the correct choice below and fill in the answer boxes to complete your choice.
A. f(x)=, for ≤ x<
, for ≤ x ≤
, for <x ≤ ,
for x< .
3. for x= -
for x>

Transcript text: Determine the domain and the range of the piecewise function shown to the right. Then write an equation for the function A. The range is a list of numbers, $\{-2,1,2\}$ (Use a comma to separate answers as needed) B. The range is $\square$ (Type your answer in interval notation) Write an equation for the function. Select the correct choice below and fill in the answer boxes to complete your choice. A. $f(x)=\left\{\begin{array}{ll}\square, & \text { for } \square \leq x<\square \\ \square, & \text { for } \square \leq x \leq \square \\ \square, & \text { for } \square$

Solution

Solution Steps

Step 1: Determine the Domain

The domain of the piecewise function is the set of all x-values for which the function is defined. From the graph, the function is defined for all x-values from -3 to 3, inclusive.

Step 2: Determine the Range

The range of the piecewise function is the set of all y-values that the function can take. From the graph, the y-values are -2, 1, and 2.

Step 3: Write the Piecewise Function

From the graph, we can see that the function has three pieces:

For $ x \leq -1 $, the function is constant at $ y = -2 $.
For $ -1 < x \leq 1 $, the function is constant at $ y = 1 $.
For $ x > 1 $, the function is constant at $ y = 2 $.

Final Answer

The domain of the function is $[-3, 3]$.

The range of the function is $\{-2, 1, 2\}$.

The piecewise function is: \[ f(x) = \begin{cases} -2 & \text{for } x \leq -1 \\ 1 & \text{for } -1 < x \leq 1 \\ 2 & \text{for } x > 1 \end{cases} \]

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